Manifold Optimization

Manifold optimization is a field focused on efficiently solving optimization problems where the solution lies on a curved surface, or manifold, rather than in a flat Euclidean space. Current research emphasizes developing algorithms that leverage the manifold's geometric structure for improved computational efficiency and accuracy, particularly in applications like federated learning and matrix factorization, often employing techniques such as Riemannian gradient descent and evolutionary metaheuristics. These advancements are impacting diverse fields, including machine learning, signal processing, and statistical analysis, by enabling faster and more robust solutions to complex problems involving high-dimensional data and non-convex optimization landscapes.